A and B are points of intersection of y=x^2-2x and y=2-3x

simultaneous equation solved = x^2 + x -2 = 0

a) Find the coordinates of A and B, given that the x coordinate of B is greater than that of A.

The line L is perpendicular to y=2-3x and passes through B.

b) Find an equation of L

The line M is parallel to y=5-3x and passes through A

c) Find an equation of M

The lime M crosses the y-axis at point P. The line L crosses the x-axis at point Q.

d) Find the distance of PQ, giving your answer in square root form where a and b are integers and b is prime. (Hint - use pythagoras' theorem)